algebra 2 6.6

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Slide 1:

ANSWER ANSWER 16 Evaluate the expression. –8 3. Expand (x – 5)2 x2 – 10x + 25 Solve the equation. 4. x2 + 6x + 9 = x + 45 (x + 9)(x – 4) = 0 x + 9 = 0 or x – 4 = 0 x = -9 x = 4 (x – 5)(x – 5) Bell Ringer WarmUps

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EXAMPLE 1 Solve a radical equation Write original equation. Cube each side to eliminate the radical. Simplify. Subtract 7 from each side. Divide each side by 2.

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EXAMPLE 1 Solve a radical equation CHECK Check x = 10 in the original equation. Substitute 10 for x. Simplify. Solution checks.

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GUIDED PRACTICE for Example 1 Solve equation. Check your solution. 1. 3√ x – 9 = –1 x = 512 x = –9 x + 25 = 16 x = 16 – 25 Check Answers!

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Standardized Test Practice EXAMPLE 3 SOLUTION 4x2/3 = 36 Write original equation. x2/3 = 9 Divide each side by 4. (x2/3)3/2 = 93/2 x = 27 Simplify. The correct answer is D. ANSWER

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Solve an equation with a rational exponent EXAMPLE 4 Solve (x + 2)3/4 – 1 = 7. (x + 2)3/4 – 1 = 7 (x + 2)3/4 = 8 x + 2 = 16 Write original equation. Add 1 to each side. Simplify. x = 14 Subtract 2 from each side.

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GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 5. 3x3/2 = 375 6. (x + 3)5/2 = 32

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GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 7. –2x3/4 = –16 8. (x – 5)5/3 = 243

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Solve an equation with an extraneous solution EXAMPLE 5 x2 + 2x + 1 = 7x + 15 x2 – 5x – 14 = 0 (x – 7)(x + 2) = 0 x – 7 = 0 or x + 2 = 0 Write original equation. Square each side. Expand left side and simplify right side. Write in standard form. Factor. Zero-product property x = 7 or x = –2 Solve for x.

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Solve an equation with an extraneous solution EXAMPLE 5 CHECK

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Solve an equation with two radicals EXAMPLE 6 = 3 – x = –2x SOLUTION Write original equation. Square each side. Expand left side and simplify right side. Isolate radical expression.

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Solve an equation with two radicals EXAMPLE 6 x + 2 = –x = ( –x)2 = x2 0 = x2 – x – 2 = (x – 2)(x + 1) 0 x – 2 = 0 x + 1 = 0 or x = 2 or x = –1 Divide each side by 2. Square each side again. Simplify. Write in standard form. Factor. Zero-product property. Solve for x.